Method for representing digitized image data

Abstract

A method for representing digitized scanned image data obtained by a non-intrusive cross-sectional image generating device. By representing an original set of user-input data points in polar coordinates, such that all of the points lie in the upper two quadrants of the coordinate system, a cubic spline algorithm can be applied once to generate a series of polynomial functions that describe a curve connecting all of the input data points. The method also uses the calculated cubic spline coefficients for the initial curve to determine intermediate data points at each of which a uniform length perpendicular is constructed. By traversing each perpendicular a desired length, new data points equidistant from the initial curve are calculated, resulting in additional curves equidistant from the initial curve. Any of the curve representations generated can then be used to select pixels from the scanned image data to display a reformatted view of the original data.

We claim: 
     
       1. A method for determining and displaying the coordinates of a curve passing through a set of initial Cartesian coordinate data points, comprising the steps of: (a) generating a two-dimensional field of image data by a non-intrusive cross-sectional image generating device;   (b) selecting a set of initial data points represented in Cartesian coordinates from the image data;   (c) converting the initial data points from Cartesian coordinates to polar coordinates such that all of the points lie in the upper quadrants of the polar coordinate system;   (d) determining a set of cubic spline polynomials describing a curve passing through each of the converted initial data points;   (e) calculating the polar coordinates of intermediate data points between the converted initial data points at a selectable resolution using the determined set of cubic spline polynomials;   (f) converting the calculated intermediate data points from polar coordinates to Cartesian coordinates; and   (g) displaying the converted intermediate data points and the initial data points on a display means as an apparent approximately continuous curve passing through the set of initial data points.   
     
     
       2. A method for determining and displaying the coordinates of an initial curve passing through a set of initial Cartesian coordinate data points, and for determining the coordinates of at leas tone additional curve equidistant from the initial curve, comprising the steps of: (a) generating a two-dimensional field of image data by a non-intrusive cross-sectional image generating device;   (b) selecting a set of initial data points represented in Cartesian coordinates from the image data;   (c) converting the initial data points from Cartesian coordinates to polar coordinates such that all of the points lie in the upper quadrants of the polar coordinate system;   (d) determining a set of cubic spline polynomials describing an initial curve passing through each of the converted initial data points;   (e) calculating the polar coordinates of intermediate data points between the converted initial data points at a selectable resolution using the determined set of cubic spline polynomials;   (e) calculating the slope of a perpendicular at selected ones of the calculated intermediate points;   (g) at each of the selected ones of the calculated intermediate points, determining and storing the coordinates of additional data points a preset distance along a line having the calculated perpendicular slope, the additional data points defining at least one curve equidistant from the initial curve;   (h) converting the calculated intermediate data points from polar coordinates to Cartesian coordinates;   (i) displaying at least the converted intermediate data points and the initial data points on a display means as an apparent approximately continuous initial curve passing through the set of initial data points.   
     
     
       3. A method for selecting and displaying image data corresponding to the intersection of (1) the coordinates of a curve passing through a set of initial Cartesian coordinate data points input by a user, with (2) image data produced in a two-dimensional field by a non-intrusive cross-sectional image generating device, comprising the steps of: (a) generating at least one set of image data representing a two-dimensional field generated by a non-intrusive cross-sectional image generating device;   (b) selecting a set of initial data points represented in Cartesian coordinates from at least one set of the image data;   (c) converting the initial data points from Cartesian coordinates to polar coordinates such that all of the points lie in the upper quadrants of the polar coordinate system;   (d) determining a set of cubic spline polynomials describing a curve passing through each of the converted initial data points;   (e) calculating the polar coordinates of intermediate data points between the converted initial data points at a selectable resolution using the determined set of cubic spline polynomials;   (f) converting the calculated intermediate data points from polar coordinates to Cartesian coordinates;   (g) addressing at leas tone of the sets of image data by selected ones of the calculated intermediate data points and initial data points;   (h) selecting the image data at each such address; and   (i) displaying the selected image data on a display means as an apparent cross-sectional image.   
     
     
       4. A method for selecting and displaying image data corresponding to the intersection of (1) the coordinates of a curve equidistant to a set of initial Cartesian coordinate data points input by a user, with (2)image data produced in a two-dimensional field by a non-intrusive cross-sectional image generating device, comprising the steps of: (a) generating at least one set of image data representing a two-dimensional field generated by a non-intrusive cross-sectional image generating device;   (b) selecting a set of initial data points represented in Cartesian coordinates from at least one set of the image data;   (c) converting the initial data points from Cartesian coordinates to polar coordinates such that all of the points lie in the upper quadrants of the polar coordinate system;   (d) determining a set of cubic spline polynomials describing an initial curve passing through each of the converted initial data points;   (e) calculating the polar coordinates of intermediate data points between the converted initial data points at a selectable resolution using the determined set of cubic spline polynomials;   (f) calculating the slope of a perpendicular at selected ones of the calculated intermediate points;   (g) at each of the selected ones of the calculated intermediate points, determining the coordinates of additional data points a preset distance along a line having the calculated perpendicular slope, the additional data points defining at least one curve equidistant from the initial curve;   (h) converting the determined additional data points defining at least one such equidistant curve from polar coordinates to Cartesian coordinates;   (i) addressing at least one of the sets of image data by selected ones of the converted additional data points;   (j) selecting the image data at each such address; and   (k) displaying the selected image data on a display means as an apparent cross-sectional image.